This article reviews formal systems that regulate persuasion dialogues. In such dialogues two or more participants aim to resolve a difference of opinion, each trying to persuade the other participants to adopt their point of view. Systems for persuasion dialogue have found application in various fields of computer science, such as non-monotonic logic, artificial intelligence and law, multi-agent systems, intelligent tutoring and computer-supported collaborative argumentation. Taking a game-theoretic view on dialogue systems, this review proposes a formal specification of the main elements of dialogue systems for persuasion and then uses it to critically review some of the main formal systems for persuasion. The focus of this review will be on regulating the interaction between agents rather than on the design and behaviour of individual agents within a dialogue.